If your reader is capable of a wi-fi connection, that doesn't mean you get free wi-fi everywhere. You'll need to connect to your home internet which you pay for and are able to set up for wi-fi; or find a free wi-fi hotspot to use, such as in Barnes & Nobles bookstores, Starbucks and other coffee shops, hotels, etc.

And you can always turn the wif-fi off if you don't want to use it. I don't know of any reader that forces it to remain on since it drains the battery faster with it on.

I have the PRS-T1 and I rarely use the wifi. You can leave it turned off if you have no need of it.
I use the wifi occasionally for downloading books directly from the Overdrive library, but you can also just download the books onto your computer and sync them to the reader.

Normally there is no cost for WiFi (unless you are traveling) and the cost for WiFi at home is free. Are you thinking of 3g? As others have said, you can turn WiFi on or off. WiFi is good though for buying books online or using libraries away from home.